TSTP Solution File: GRP590-1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : GRP590-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 21:04:23 EDT 2024
% Result : Unsatisfiable 127.76s 20.68s
% Output : Refutation 127.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 25 unt; 5 typ; 0 def)
% Number of atoms : 39 ( 38 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 322 ( 14 ~; 7 |; 0 &; 301 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 ^ 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(b2_type,type,
b2: $i ).
thf(a2_type,type,
a2: $i ).
thf(double_divide_type,type,
double_divide: $i > $i > $i ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( inverse @ ( double_divide @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( inverse @ ( double_divide @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( inverse @ ( double_divide @ B @ A ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
thf(4,plain,
( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,plain,
( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 ),
inference(lifteq,[status(thm)],[5]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( ( multiply @ ( inverse @ ( double_divide @ B @ A ) ) @ a2 )
!= a2 )
| ( ( multiply @ A @ B )
!= ( multiply @ ( inverse @ b2 ) @ b2 ) ) ),
inference(paramod_ordered,[status(thm)],[10,6]) ).
thf(14,plain,
( ( multiply @ ( inverse @ ( double_divide @ b2 @ ( inverse @ b2 ) ) ) @ a2 )
!= a2 ),
inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( inverse @ b2 )),bind(B,$thf( b2 ))]]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @ B )
= C ),
inference(lifteq,[status(thm)],[7]) ).
thf(47,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( double_divide @ ( inverse @ ( double_divide @ C @ ( inverse @ ( double_divide @ D @ ( inverse @ F ) ) ) ) ) @ E )
= F )
| ( ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @ B )
!= ( double_divide @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[8,8]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( double_divide @ ( inverse @ ( double_divide @ D @ ( inverse @ ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ C @ B ) @ ( inverse @ ( double_divide @ C @ ( inverse @ D ) ) ) ) ) @ ( inverse @ A ) ) ) ) ) @ B )
= A ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( O )),bind(D,$thf( inverse @ ( double_divide @ ( double_divide @ M @ K ) @ ( inverse @ ( double_divide @ M @ ( inverse @ O ) ) ) ) )),bind(E,$thf( K )),bind(F,$thf( F ))]]) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( double_divide @ ( inverse @ ( double_divide @ D @ ( inverse @ ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ C @ B ) @ ( inverse @ ( double_divide @ C @ ( inverse @ D ) ) ) ) ) @ ( inverse @ A ) ) ) ) ) @ B )
= A ),
inference(simp,[status(thm)],[48]) ).
thf(550,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( double_divide @ ( inverse @ ( double_divide @ G @ ( inverse @ C ) ) ) @ E )
= D )
| ( ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @ B )
!= ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ F @ E ) @ ( inverse @ ( double_divide @ F @ ( inverse @ G ) ) ) ) ) @ ( inverse @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,57]) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( inverse @ ( double_divide @ A @ ( inverse @ A ) ) ) @ ( inverse @ B ) )
= B ),
inference(pattern_uni,[status(thm)],[550:[bind(A,$thf( A )),bind(B,$thf( inverse @ H )),bind(C,$thf( C )),bind(D,$thf( H )),bind(E,$thf( inverse @ H )),bind(F,$thf( A )),bind(G,$thf( C ))]]) ).
thf(634,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( inverse @ ( double_divide @ A @ ( inverse @ A ) ) ) @ ( inverse @ B ) )
= B ),
inference(simp,[status(thm)],[551]) ).
thf(698,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( double_divide @ ( inverse @ ( double_divide @ F @ ( inverse @ B ) ) ) @ D )
= C )
| ( ( double_divide @ ( inverse @ ( double_divide @ A @ ( inverse @ A ) ) ) @ ( inverse @ B ) )
!= ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ E @ D ) @ ( inverse @ ( double_divide @ E @ ( inverse @ F ) ) ) ) ) @ ( inverse @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[634,57]) ).
thf(699,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( inverse @ ( double_divide @ B @ ( inverse @ A ) ) ) @ ( inverse @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[698:[bind(A,$thf( double_divide @ G @ ( inverse @ I ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( inverse @ I )),bind(E,$thf( G )),bind(F,$thf( I ))]]) ).
thf(802,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( inverse @ ( double_divide @ B @ ( inverse @ A ) ) ) @ ( inverse @ B ) )
= A ),
inference(simp,[status(thm)],[699]) ).
thf(1143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( double_divide @ ( multiply @ A @ B ) @ ( inverse @ D ) )
= C )
| ( ( inverse @ ( double_divide @ B @ A ) )
!= ( inverse @ ( double_divide @ D @ ( inverse @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,802]) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( multiply @ ( inverse @ B ) @ A ) @ ( inverse @ A ) )
= B ),
inference(pattern_uni,[status(thm)],[1143:[bind(A,$thf( inverse @ E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( multiply @ ( inverse @ B ) @ A ) @ ( inverse @ A ) )
= B ),
inference(simp,[status(thm)],[1144]) ).
thf(1632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( double_divide @ ( inverse @ B ) @ ( inverse @ D ) )
= C )
| ( ( double_divide @ ( multiply @ ( inverse @ B ) @ A ) @ ( inverse @ A ) )
!= ( double_divide @ D @ ( inverse @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1234,802]) ).
thf(1633,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( inverse @ B ) @ ( inverse @ ( multiply @ ( inverse @ B ) @ A ) ) )
= A ),
inference(pattern_uni,[status(thm)],[1632:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( multiply @ ( inverse @ G ) @ F ))]]) ).
thf(1735,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( inverse @ B ) @ ( inverse @ ( multiply @ ( inverse @ B ) @ A ) ) )
= A ),
inference(simp,[status(thm)],[1633]) ).
thf(24117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( double_divide @ ( inverse @ B ) @ ( inverse @ ( multiply @ ( inverse @ B ) @ A ) ) )
!= ( double_divide @ ( inverse @ ( double_divide @ C @ ( inverse @ C ) ) ) @ ( inverse @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[1735,634]) ).
thf(24118,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ ( double_divide @ B @ ( inverse @ B ) ) ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[24117:[bind(A,$thf( I )),bind(B,$thf( double_divide @ M @ ( inverse @ M ) )),bind(C,$thf( M )),bind(D,$thf( multiply @ ( inverse @ ( double_divide @ M @ ( inverse @ M ) ) ) @ I ))]]) ).
thf(24521,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ ( double_divide @ B @ ( inverse @ B ) ) ) @ A )
= A ),
inference(simp,[status(thm)],[24118]) ).
thf(25857,plain,
a2 != a2,
inference(rewrite,[status(thm)],[14,24521]) ).
thf(25858,plain,
$false,
inference(simp,[status(thm)],[25857]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP590-1 : TPTP v8.2.0. Released v2.6.0.
% 0.17/0.17 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n013.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sun May 19 04:53:09 EDT 2024
% 0.25/0.38 % CPUTime :
% 1.06/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.06 % [INFO] Parsing done (104ms).
% 1.33/1.06 % [INFO] Running in sequential loop mode.
% 1.76/1.28 % [INFO] nitpick registered as external prover.
% 1.76/1.28 % [INFO] Scanning for conjecture ...
% 1.92/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.92/1.35 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.92/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 1.92/1.36 % [INFO] Type checking passed.
% 1.92/1.36 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 127.76/20.68 % [INFO] Killing All external provers ...
% 127.76/20.68 % Time passed: 20104ms (effective reasoning time: 19610ms)
% 127.76/20.68 % Axioms used in derivation (2): multiply, single_axiom
% 127.76/20.68 % No. of inferences in proof: 32
% 127.76/20.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 20104 ms resp. 19610 ms w/o parsing
% 127.76/20.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 127.76/20.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------